This book was written to serve as a graduate-level textbook for special topics classes in mathematics, statistics, and economics, to introduce these topics to other researchers, and for use in short courses. It is an introduction to the theory of majorization and related notions, and contains detailed material on economic applications of majorization and the Lorenz order, investigating the theoretical aspects of these two interrelated orderings. Revising and expanding on an earlier monograph, Majorization and the Lorenz Order: A Brief Introduction, the authors provide a straightforward development and explanation of majorization concepts, addressing historical development of the topics, and providing up-to-date coverage of families of Lorenz curves. The exposition of multivariate Lorenz orderings sets it apart from existing treatments of these topics. Mathematicians, theoretical statisticians, economists, and other social scientists who already recognize the utility of the Lorenz order in income inequality contexts and arenas will find the book useful for its sound development of relevant concepts rigorously linked to both the majorization literature and the even more extensive body of research on economic applications. Barry C. Arnold, PhD, is Distinguished Professor in the Statistics Department at the University of California, Riverside. He is a Fellow of the American Statistical Society, the American Association for the Advancement of Science, and the Institute of Mathematical Statistics, and is an elected member of the International Statistical Institute. He is the author of more than two hundred publications and eight books. Jose Maria Sarabia, PhD, is Professor of Statistics and Quantitative Methods in Business and Economics in the Department of Economics at the University of Cantabria, Spain. He is author of more than one hundred and fifty publications and ten books and is an associate editor of several journals including TEST, Communications in Statistics, and Journal of Statistical Distributions and Applications.

This handbook serves as a comprehensive, systematic reference to the major mathematical models used in radio engineering and communications, and presents computer simulation algorithms to help the reader estimate parameters of radio systems. It provides the technical details necessary to design and analyze radar, communication, radio navigation, radio control, electronic intelligence and electronic warfare systems. Mathcad routines, cited in the handbook, should help the reader to optimize radar system performance analysis, and can be used to create custom-made software that better answers specific needs.

Going far beyond the standard texts, this book extensively covers boundary integral equation (BIE) formulations and the boundary element method (BEM). The first section introduces BIE formulations for potential and elasticity problems, following the modern regularization approach - the fundamental starting point for research in this field. Secondly, a clear description of BIE formulations for wave and elastodynamics problems, in both time and frequency domains is presented. Finally, recent research in the field, related to variational integral formulations, use of geometrical symmetry, shape sensitivity and fracture mechanics is summarised. Within the text a broad range of application areas, industrial as well as research related, are examined. These include:

• elasticity and small-strain elastoplasticity
• time-domain and frequency-domain scalar and elastic waves
• fracture mechanics

This book is the first part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton's research. Each article is accompanied by comments from an expert on the respective topic, which serves to situate the article in its proper context, to successfully link past, present and hopefully future developments of the theory, and to help readers grasp the extent of Kalton's accomplishments. Kalton's work represents a bridge to the mathematics of tomorrow, and this book will help readers to cross it. Nigel Kalton (1946-2010) was an extraordinary mathematician who made major contributions to an amazingly diverse range of fields over the course of his career.

This book focuses on the finite-time control of attitude stabilization, attitude tracking for individual spacecraft, and finite-time control of attitude synchronization. It discusses formation reconfiguration for multiple spacecraft in complex networks, and provides a new fast nonsingular terminal sliding mode surface (FNTSMS). Further, it presents newly designed controllers and several control laws to enhance the performance of spacecraft systems and meet related demands, such as strong disturbance rejection and high-precision control. As such, the book establishes a fundamental framework for these topics, while also highlighting the importance of integrated analysis. It is a useful resource for all researchers and students who are interested in this field, as well as engineers whose work involves designing flight vehicles.

This book presents in detail an alternative approach to solving problems involving both linear and nonlinear oscillations of elastic distributed parameter systems. It includes the so-called variational, projection and iterative gradient methods, which, when applied to nonlinear problems, use the procedure of linearization of the original non-linear equations. These methods are not universal and require a different solution for each problem or class of problems.However, in many cases the combination of the methods shown in this book leads to more efficient algorithms for solving important applied problems.To record these algorithms in a unified form, the first part of the book and its appendix devote considerable attention to compiling the general operator equations, which include (as particular cases) equations for vibrations in rods, plates, shells and three-dimensional bodies. They are mainly considered to be periodic or nearly periodic oscillations, which correspond to stat ionary or nearly stationary regimes of machinery operation. In turn, the second part of the book presents a number of solutions for selected applications.

This book addresses a broad range of problems commonly encountered in the fields of financial analysis, logistics and supply chain management, such as the use of big data analytics in the banking sector. Divided into twenty chapters, some of the contemporary topics discussed in the book are co-operative/non-cooperative supply chain models for imperfect quality items with trade-credit financing; a non-dominated sorting water cycle algorithm for the cardinality constrained portfolio problem; and determining initial, basic and feasible solutions for transportation problems by means of the "supply demand reparation method" and "continuous allocation method." In addition, the book delves into a comparison study on exponential smoothing and the Arima model for fuel prices; optimal policy for Weibull distributed deteriorating items varying with ramp type demand rate and shortages; an inventory model with shortages and deterioration for three different demand rates; outlier labeling methods for medical data; a garbage disposal plant as a validated model of a fault-tolerant system; and the design of a "least cost ration formulation application for cattle"; a preservation technology model for deteriorating items with advertisement dependent demand and trade credit; a time series model for stock price forecasting in India; and asset pricing using capital market curves. The book offers a valuable asset for all researchers and industry practitioners working in these areas, giving them a feel for the latest developments and encouraging them to pursue further research in this direction.

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

As the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS15), the proceedings of CoMFoS16 present further advances and new topics in mathematical theory and numerical simulations related to various aspects of continuum mechanics. These include fracture mechanics, shape optimization, modeling of earthquakes, material structure, interface dynamics and complex systems.. The authors are leading researchers with a profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry. The book helps readers to understand how mathematical theory can be applied to various industrial problems, and conversely, how industrial problems lead to new mathematical challenges.

This multi-contributed volume provides a practical, applications-focused introduction to nonlinear acoustical techniques for nondestructive evaluation. Compared to linear techniques, nonlinear acoustical/ultrasonic techniques are much more sensitive to micro-cracks and other types of small distributed damages. Most materials and structures exhibit nonlinear behavior due to the formation of dislocation and micro-cracks from fatigue or other types of repetitive loadings well before detectable macro-cracks are formed. Nondestructive evaluation (NDE) tools that have been developed based on nonlinear acoustical techniques are capable of providing early warnings about the possibility of structural failure before detectable macro-cracks are formed. This book presents the full range of nonlinear acoustical techniques used today for NDE. The expert chapters cover both theoretical and experimental aspects, but always with an eye towards applications. Unlike other titles currently available, which treat nonlinearity as a physics problem and focus on different analytical derivations, the present volume emphasizes NDE applications over detailed analytical derivations. The introductory chapter presents the fundamentals in a manner accessible to anyone with an undergraduate degree in Engineering or Physics and equips the reader with all of the necessary background to understand the remaining chapters. This self-contained volume will be a valuable reference to graduate students through practising researchers in Engineering, Materials Science, and Physics. Represents the first book on nonlinear acoustical techniques for NDE applications Emphasizes applications of nonlinear acoustical techniques Presents the fundamental physics and mathematics behind nonlinear acoustical phenomenon in a simple, easily understood manner Covers a variety of popular NDE techniques based on nonlinear acoustics in a single volume

This thesis presents a pioneering method for gleaning the maximum information from the deepest images of the far-infrared universe obtained with the Herschel satellite, reaching galaxies fainter by an order of magnitude than in previous studies. Using these high-quality measurements, the author first demonstrates that the vast majority of galaxy star formation did not take place in merger-driven starbursts over 90% of the history of the universe, which suggests that galaxy growth is instead dominated by a steady infall of matter. The author further demonstrates that massive galaxies suffer a gradual decline in their star formation activity, providing an alternative path for galaxies to stop star formation. One of the key unsolved questions in astrophysics is how galaxies acquired their mass in the course of cosmic time. In the standard theory, the merging of galaxies plays a major role in forming new stars. Then, old galaxies abruptly stop forming stars through an unknown process. Investigating this theory requires an unbiased measure of the star formation intensity of galaxies, which has been unavailable due to the dust obscuration of stellar light.

Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, is a volume undertaken by the friends and colleagues of Sid Yakowitz in his honor. Fifty internionally known scholars have collectively contributed 30 papers on modeling uncertainty to this volume. Each of these papers was carefully reviewed and in the majority of cases the original submission was revised before being accepted for publication in the book. The papers cover a great variety of topics in probability, statistics, economics, stochastic optimization, control theory, regression analysis, simulation, stochastic programming, Markov decision process, application in the HIV context, and others. There are papers with a theoretical emphasis and others that focus on applications. A number of papers survey the work in a particular area and in a few papers the authors present their personal view of a topic. It is a book with a considerable number of expository articles, which are accessible to a nonexpert - a graduate student in mathematics, statistics, engineering, and economics departments, or just anyone with some mathematical background who is interested in a preliminary exposition of a particular topic. Many of the papers present the state of the art of a specific area or represent original contributions which advance the present state of knowledge. In sum, it is a book of considerable interest to a broad range of academic researchers and students of stochastic systems.

The aim of this book is to give a physical treatment of the kinetic theory of gases and magnetoplasmas, covering the standard material in as simple a way as possible, using mean-free-path arguments when possible and identifying problem areas where received theory has either failed or has fallen short of expectations. Examples are provided by strong shock waves, ultrasonic waves (high Knudsen numbers), and transport across strong magnetic fields. Examples of problem areas provided by strong shock waves, ultrasonic waves (high Knudsen numbers), and transport across strong magnetic fields. One of the paradoxes arising in kinetic theory concerns the fluid pressure. Collisions are necessary for a fluid force to result, yet standard kinetic theory does not entail this, being satisfied to bypass Newton's equations by defining pressure as a momentum flux. This omission usually has no adverse consequences, but with increasing Knudsen number, it leads to errors. This text pays particular attention to pressure, explaining the importance of allowing for its collisional nature from the outset in developing kinetic theory.

This thesis proposes a reliable and repeatable method for implementing Spoof Surface Plasmon (SSP) modes in the design of various circuit components. It also presents the first equivalent circuit model for plasmonic structures, which serves as an insightful guide to designing SSP-based circuits. Today, electronic circuits and systems are developing rapidly and becoming an indispensable part of our daily life; however the issue of compactness in integrated circuits remains a formidable challenge. Recently, the Spoof Surface Plasmon (SSP) modes have been proposed as a novel platform for highly compact electronic circuits. Despite extensive research efforts in this area, there is still an urgent need for a systematic design method for plasmonic circuits. In this thesis, different SSP-based transmission lines, antenna feeding networks and antennas are designed and experimentally evaluated. With their high field confinement, the SSPs do not suffer from the compactness limitations of traditional circuits and are capable of providing an alternative platform for the future generation of electronic circuits and electromagnetic systems.

This book is a collection of papers presented at the 23rd International Conference on Domain Decomposition Methods in Science and Engineering, held on Jeju Island, Korea on July 6-10, 2015. Domain decomposition methods solve boundary value problems by splitting them into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. Domain decomposition methods have considerable potential for a parallelization of the finite element methods, and serve a basis for distributed, parallel computations.

An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.
Key Features
* This is an introductory treatise on wavelet analysis, with an emphasis on spline-wavelets and time-frequency analysis
* This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis
* Suitable as a textbook for a beginning course on wavelet analysis

This prizewinning PhD thesis presents a general discussion of the orbital motion close to solar system small bodies (SSSBs), which induce non-central asymmetric gravitational fields in their neighborhoods. It introduces the methods of qualitative theory in nonlinear dynamics to the study of local/global behaviors around SSSBs. Detailed mechanical models are employed throughout this dissertation, and specific numeric techniques are developed to compensate for the difficulties of directly analyzing. Applying this method, several target systems, like asteroid 216 Kleopatra, are explored in great detail, and the results prove to be both revealing and pervasive for a large group of SSSBs.

This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity w. In particular, an extensive account is given of structural, limiting, and extremal properties of perfect w-splines generalizing standard polynomial perfect splines in the theory of Sobolev classes. In this context special attention is paid to the qualitative description of Chebyshev w-splines and w-polynomials associated with the Kolmogorov problem of n-widths and sharp additive inequalities between the norms of intermediate derivatives in functional classes with a bounding modulus of continuity. Since, as a rule, the techniques of the theory of Sobolev classes are inapplicable in such classes, novel geometrical methods are developed based on entirely new ideas. The book can be used profitably by pure or applied scientists looking for mathematical approaches to the solution of practical problems for which standard methods do not work. The scope of problems treated in the monograph, ranging from the maximization of integral functionals, characterization of the structure of equimeasurable functions, construction of Chebyshev splines through applications of fixed point theorems to the solution of integral equations related to the classical Euler equation, appeals to mathematicians specializing in approximation theory, functional and convex analysis, optimization, topology, and integral equations

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This book presents selected papers from the 3rd International Workshop on Computational Engineering held in Stuttgart from October 6 to 10, 2014, bringing together innovative contributions from related fields with computer science and mathematics as an important technical basis among others. The workshop discussed the state of the art and the further evolution of numerical techniques for simulation in engineering and science. We focus on current trends in numerical simulation in science and engineering, new requirements arising from rapidly increasing parallelism in computer architectures, and novel mathematical approaches. Accordingly, the chapters of the book particularly focus on parallel algorithms and performance optimization, coupled systems, and complex applications and optimization.

This book introduces readers to MesoBioNano (MBN) Explorer - a multi-purpose software package designed to model molecular systems at various levels of size and complexity. In addition, it presents a specially designed multi-task toolkit and interface - the MBN Studio - which enables the set-up of input files, controls the simulations, and supports the subsequent visualization and analysis of the results obtained. The book subsequently provides a systematic description of the capabilities of this universal and powerful software package within the framework of computational molecular science, and guides readers through its applications in numerous areas of research in bio- and chemical physics and material science - ranging from the nano- to the mesoscale. MBN Explorer is particularly suited to computing the system's energy, to optimizing molecular structure, and to exploring the various facets of molecular and random walk dynamics. The package allows the use of a broad variety of interatomic potentials and can, e.g., be configured to select any subset of a molecular system as rigid fragments, whenever a significant reduction in the number of dynamical degrees of freedom is required for computational practicalities. MBN Studio enables users to easily construct initial geometries for the molecular, liquid, crystalline, gaseous and hybrid systems that serve as input for the subsequent simulations of their physical and chemical properties using MBN Explorer. Despite its universality, the computational efficiency of MBN Explorer is comparable to that of other, more specialized software packages, making it a viable multi-purpose alternative for the computational modeling of complex molecular systems. A number of detailed case studies presented in the second part of this book demonstrate MBN Explorer's usefulness and efficiency in the fields of atomic clusters and nanoparticles, biomolecular systems, nanostructured materials, composite materials and hybrid systems, crystals, liquids and gases, as well as in providing modeling support for novel and emerging technologies. Last but not least, with the release of the 3rd edition of MBN Explorer in spring 2017, a free trial version will be available from the MBN Research Center website (mbnresearch.com).

This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.

Reliability is one of the fundamental criteria in engineering systems. Design and maintenance serve to support it throughout the systems life. As such, maintenance acts in parallel to production and can have a great impact on the availability and capacity of production and the quality of the products. The authors describe current and innovative methods useful to industry and society.

Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.
Key Features
* A self-contained, prgamatic exposition of the needed elements of random variable theory
* Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations
* Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples
* Clear treatments of first passages, first exits, and stable state fluctuations and transitions
* Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics

This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis. Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent programs. The state space of a concurrent program is described as a higher-dimensional space, the topology of which encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than "just" the topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a result, tools and concepts from topology have to be extended to take privileged directions into account. The target audience for this book consists of graduate students, researchers and practitioners in the field, mathematicians and computer scientists alike.